Sage Mode - a way of engrossing oneself in/with natural energy.
Sage Arts - an art/technique of using natural energy.
You don't need to be in Sage Mode in order to use Sage Arts, but Sage Arts are much more effective in Sage Mode.
I'm not sure what do you mean...?
Wait, are you implying that Hashirama normally has tattoos on his forehead, around his eyes and all over his face ? He is still shown gathering energy, it's just that he has a different position, it's possible that Jiraya as well took a different position in order to gather Natural Energy, from the one that Naruto takes. Basically, it doesn't matter what position they take, as long as they are truly motionless.
...maybe, I'm not sure, since Hashirama already has the 3rd legendary Sage Mode, so well it... no I take it back . I almost forgot that each of the Sage Mode types had at least 2 known users in the series (Frog: Jiraya, Naruto; Snake: Oro, Kabuto: 3rd: Hashirama, Sakura?/Tsunade?).
I guess that the fact that Haruno clan symbol is exactly the same like the one that appears on Hashirama's forehead when he enters Sage Mode, can mean something and there might be a connection. Still, seeing as neither Jiray nor Oro had a perfect Sago Mode (though Jiraya went further with his studies in this regard) then the same would mean for Tsunade and seeing as Hashirama has a perfect one, Sakura's might not be a perfect one (I would rather like to see her Supreme Chakra Control to play again, but not like Tsunade, to heal, but one that condenses her chakra - similar like in the fist but better - into each of her cells, making her pretty much Ultra Human surpassing those with Super Human Strength).
Now that I mentioned Sage Mode types, then assuming that there are only 3 and that 4th Kazekage's marks weren't an effect of the Kekkei Genkai, then I would have to say that Garaa and his Dad are blood related to Jyugo's clan, but their effect is very limited and only effects appear around their eyes (this means that Garaa is constantly using a bit of Natural Energy or something like that, plus Garaa's red hair is a prove of being Uzumaki so this goes quite nicely with his capabilities in this department).